Question 133369
Remember {{{(g o f)(x)=g(f(x))}}}




*[Tex \LARGE (g o f)(x)=g\left(f(x)\right)] Start with the given property


*[Tex \LARGE g\left(f(x)\right)=2\left(\frac{1}{2}x+5\right) -1] Plug in {{{f(x)=(1/2)x+5}}} into each x of {{{g(x)=2x -1}}}




*[Tex \LARGE g\left(f(x)\right)=2\left(\frac{1}{2}\right)x+2*5 -1] Distribute



*[Tex \LARGE g\left(f(x)\right)=\frac{2}{2}x+10 -1] Multiply 



*[Tex \LARGE g\left(f(x)\right)=x+10 -1] Reduce



*[Tex \LARGE g\left(f(x)\right)=x+9] Combine like terms